Half-life of a substance is 10 years. In what | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The radioactive decay law is given by $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$,where $N$ is the remaining amount,$N_0$ is the initial amou

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) The radioactive decay law is given by $N = N_0 \left( \frac{1}{2} ight)^{t/T_{1/2}}$,where $N$ is the remaining amount,$N_0$ is the initial amount,$t$ is the time elapsed,and $T_{1/2}$ is the half-life.Given $T_{1/2} = 10 	ext{ years}$ and $N = \frac{1}{4} N_0$.Substituting these values: $\frac{1}{4} N_0 = N_0 \left( \frac{1}{2} ight)^{t/10}$.$\frac{1}{4} = \left( \frac{1}{2} ight)^{t/10}$.Since $\frac{1}{4} = \left( \frac{1}{2} ight)^2$,we have $\left( \frac{1}{2} ight)^2 = \left( \frac{1}{2} ight)^{t/10}$.Comparing the exponents: $2 = \frac{t}{10}$.Therefore,$t = 20 	ext{ years}$.

Half-life of a substance is $10$ years. In what time,it becomes $\frac{1}{4}$ of the initial amount?

Similar Questions

$A$ radioactive sample has a half-life of $5$ years. The percentage of the fraction decayed in $10$ years will be (in $\%$)

$A$ radioactive material has a half-life of $10$ days. What fraction of the material would remain after $30$ days?

Half-life of a radioactive element is $10 \, days$. The time during which the quantity remains $1/10$ of the initial mass will be ......... $days$.

The counting rate observed from a radioactive source at $t=0$ second was $1600$ counts per second and at $t=8$ seconds it was $100$ counts per second. The counting rate observed,as counts per second at $t=6$ seconds,will be

Half-lives of two radioactive substances $A$ and $B$ are,respectively,$20 \ min$ and $40 \ min$. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \ min$,the ratio of the remaining number of $A$ and $B$ nuclei is

Vedclass Test Series

Exam Paper Generator

Online Exam Module